KappaTau curves are a type of space curve. Instead of describing
the curve in terms of (x,y,z) coordinates, the curve is described
by its intrinsic geometry. That is, its curvature (kappa)
and its torsion or twisting (tau) are given as functions of the
arclength along the curve. You can read Rucker's paper about
this topic online here: "Watching
Flies Fly: Kappa Tau Space Curves" A similar article
titled “How Flies Fly: The Curvature and Torsion of Space
Curves,” is to appear in a book of articles honoring Martin
Gardner, tentatively titled Puzzler’s Tribute, to be published
by A K Peters, Ltd.

KappaTau is a Windows program which shows space curves defined
in terms of curvature (kappa) and torsion (tau). The KAPTAU.ZIP
file is 103K big, and it includes KAPTAU.EXE, KAPTAU.HLP, and a
support file called BWCC.DLL. The curves tumble in space and you
can do a virtual reality fly-through with left and right clicks
of your mouse.

The KappaTau program was discovered using the Mathematica software.
A copy of Rucker's Mathematica notebook for this is available here.
The KT_MATH.ZIP file is 750K big. It includes three versions of
the Mathematica notebook: KTMAC.MA for Mathematica 1.0 on the Mac,
KT10.MA for Mathematica 2.0 in Windows, and KT10_FIX.MA for Mathematica
3.0 on Windows.

“Designing a Baseball
Cover,” An article by Richard B. Thompson about the “true”
baseball strich curve (which resembles, but is different from, the
kappatau curve shown in the background of the KappaTau Downloads
page).